Tim's recent lengthy return to the Sakai paper clip top at 2:33...

https://youtu.be/tErDu8cQtCc BTW, there is no need to balance AMIs around an asymmetric top. All you need is dynamic (static+couple) balance about the intended spin axis. Meaning that the spin axis must pass exactly through the top's CM and align perfectly with its greatest or least principal axis.

Ultimately, this follows from 4 facts:

1. Mass is always positive.

2. Moments of inertia are always positive.

3. Moments about the same axis add (build up).

4. In the absence of air and tip resistance, two tops with identical

~~mass properties (mass, ~~principal axes of inertia, principal moments of inertia, and CM location

~~)~~ will behave

*exactly* the same -- though still with considerable room to differ in mass, size, and shape.

A key consequence: The AMI of a point mass M orbiting an axis at radius R is

*identical* to the AMI of a very thin circular ring of mass M and radius R centered on that axis, regardless of the ring's axial length.

In other words, AMI knows only about the squares of the distances from the spin axis to all the contributing masses -- and nothing about either their azimuths around the axis, or their locations along the axis. (On that last point, TMI is a very different story.)

So there's no way for the AMI contribution of one part of a top to offset the AMI contribution of any other. Which makes the idea of AMI balance meaningless.

Contributions to CM location combine in a totally different way -- one in which balance

*does* make sense. Look up first and second mass moments to see why.